Tom tells Julia that Michael has given him a box for the opening of the new play. When we see Tom after Julia makes an obvious reference to him by saying, "B-E-N," he is seated not in a box but in the orchestra section, next to Julia's son and in front of Julia's male friend.
When Julia visits Tom's flat the first time, he stands back to let her go up the stairs first. When we see them climbing the stairs, he is now in front, and again stops and lets her go in front of him to enter the flat.
When Tom first dances with Julia in a nightclub, he is clearly seen wearing a square-faced wristwatch. This is the Cartier given to him a few scenes later by Julia. He shouldn't be wearing a watch at all in this early scene, having pawned his own round-faced watch to pay for the night's entertainment.
Michael hands Julia a beer bottle that he opened by twisting off the cap; this innovation wasn't introduced until the mid-1960s.
There is a modern plastic identification ear tag in the jersey cow.
The picture frame that Julia picks up from the piano on stage has plastic hanging hooks on the back in a style and manufacturing method which would not have been available in 1938 England.